The shelf life of many food products is dependant on the oxygen transmission rate (OTR) of the material used to package the food. This is especially true during long-term storage. The presence of oxygen leads to many reactions that can decrease the shelf life of many foods. Microbial growth, oxidation of lipids causing rancidity, and senescence of fruits and vegetables all require oxygen to take place. Thus, it is important to the food industry that the OTR of packaging materials are consistent with the needs of products.
Attempts to predict transmission rates of gases through perforated films and other types of semi-barrier materials have been made. Emond et al. (1991) and Fonseca et al. (1996) used empirical models to describe diffusion of gases through perforated films. Also, Fishman et al. (1996) modeled transmission rates of gases using Fick's law of diffusion, while Hirata et al. used Graham's law of diffusion. Renault (1994) modeled diffusion of gas through perforated films with Maxwell Stefan's law. Ghosh and Anantheswaran (1998) determined that models based on Fick's law were in closest agreement with experimental data.
Oxygen transfer rate of perforated film depends on two mechanisms including permeation of oxygen through the base film and diffusion of oxygen through the perforations. Total flow through the film was described by Fishman et al. (1996) as:F=JA+JhAh  (1)where A is the total area of the film, J is the flux of oxygen through the film, Ah is the total area of the holes, and Jh is the flux of gas through a unit area of a hole.
Permeation of gas through film is given by:
                    J        =                              -                          P              ⁡                              (                                                      p                    i                                    -                                      p                    A                                                  )                                              L                                    (        2        )            where P is the permeability of the film, L is film thickness, pi is partial pressure of oxygen inside the package and pA is partial pressure of oxygen in the atmosphere surrounding the package.
Diffusion of oxygen through perforations should obey Fick's Law:
                              J          h                =                              -                          D              ⁡                              (                                  p                  -                                      p                    A                                                  )                                                          L            h                                              (        3        )            where D is the diffusion coefficient of gas in air through the perforation and Lh is the diffusion path length. If the distance between perforations is much greater than the radius of the perforation, then Lh can be approximated by the model employed by Meidner and Mansfield (1968) and Nobel (1974) for stomatal resistance.Lh=L+Rh  (4)where Rh is the radius of the hole. Combining equations (1), (2), (3), and (4) yields
                    F        =                              (                                          p                A                            -              p                        )                    ⁡                      [                                          AP                L                            +                                                                    A                    h                                    ⁢                  D                                                  L                  +                                      R                    h                                                                        ]                                              (        5        )            
As an alternative to predicting an oxygen transmission rate (OTR), measurement of OTR of plastic packaging films and other semi-barrier materials can also be utilized for studying modified atmosphere packages (MAP). Typical existing methods to measure the OTR of a material involve passing an oxygen-containing gas and an oxygen-free gas on either side of the material. Oxygen moves through the material by permeation and is picked up by the oxygen-free gas, which flows to a sensor. In many cases, the sensor is a coulometric device. These methods do not work well with perforated films, though, because slight variations in gas flow rates or pressures on either side of the material can cause gas to flow through the perforations by convective mass-transfer. This can cause the measured OTR to be higher or lower than the actual OTR, depending on factors such as which side has the greater flow rate. To overcome these problems, the flow rates and pressures can be set and monitored very precisely, but this can be very expensive.
In addition, few commercially available films have sufficiently high oxygen transmission rates for packaging of respiring products. Many fruits and vegetables, such as strawberries and mangos have high respiration rates that make it difficult to supply sufficient oxygen through packaging films without perforations. Films with perforations having diameters on the order of 40 to 250 μm are generally referred to as microperforated films.
The use of perforated films in packaging materials is very common, especially with fresh-cut fruits and vegetables. However, design of packages using microperforated films has been difficult due to lack of methods capable of properly measuring OTR of films with perforations. In particular, the OTR of microperforated film depends on multiple factors including permeability of the film, perforation geometry, film thickness, and number of perforations in a given area of film. U.S. Pat. Nos. 6,422,063, 6,834,532, and 7,004,010 each describe methods for measuring the OTR of a perforated material. However, none of these methods is convenient, accurate, and cost-effective.
Difficulties measuring OTR of perforated films with traditional approaches is readily evident. Traditional methods include manometric, volume, coulometric, and concentration increase methods. For manometric and volume methods, a sample is typically mounted in a gas transmission cell to form a sealed semibarrier between two chambers. One chamber contains test gas at a specific high pressure, and the other chamber, which is at a lower pressure, receives the permeating gas. In the manometric method, the lower pressure chamber is evacuated and transmission of the gas through the film is indicated by an increase in pressure. In the volume method, the lower pressure chamber is maintained at atmospheric pressure and the gas transmission is indicated by a change in volume.
The coulometric method, an example of which is illustrated in FIG. 1, involves mounting a specimen as a sealed semi-barrier between two chambers at atmospheric pressure. Referring to FIG. 1, instrumentation supplied by Mocon, Inc. (Minneapolis, Minn.) for implementing the coulometric approach is shown. FIG. 1 shows a procedure where oxygen would permeate from the right outer chamber test cell to left inner chamber test cell through the test film mounted between them. Here, the test film splits the test chamber into two halves. An oxygen containing gas (test gas) flows through the outer chamber test cell while an oxygen free gas (carrier gas) flows through the inner chamber test cell. The inner chamber is purged with a non-oxygen containing carrier gas, such as nitrogen, and the other chamber is purged with an oxygen containing test gas, which is typically ambient air (21% oxygen) or 100% oxygen. Oxygen permeates through the film into the carrier gas, which is then transported to a coulometric sensor. Oxygen is consumed in a process that generates an electric current proportional to the amount of oxygen flowing to the sensor in a given time period.
This coulometric system works well for film samples without perforations since slight variations of pressure on either side of the sample do not significantly alter measurements. However, with perforated films, variations in pressure can cause gas to flow freely from one side to the other, which directly affects oxygen measurements.
The concentration increase method, illustrated, for example, in FIG. 2, is an unsteady state method where the chamber is sealed with a semi-barrier and is initially purged with an oxygen free gas such as, for example, nitrogen. Oxygen diffuses through the barrier film and/or perforations, and the concentration of oxygen in the chamber is measured over time. The most common method used to measure the oxygen concentration is a gas chromatograph, which requires removal of gas samples from the test chamber, as illustrated by use of the syringe in FIG. 2. FIG. 2 shows a method for measuring OTR that requires headspace sampling over time (unsteady state measurement of headspace over time). Actual experiments often require removal of multiple samples from a single test specimen. Without perforations, each sampling changes headspace volume, which affects the measurement. With perforations, each sample draws new gas into the headspace so as to change gas compositions, thus affecting subsequent samples.
Accordingly, there exists a need in the art for a more convenient, accurate, and cost-effective method to measure the oxygen transmission rate of a material.